It is well known that thermoplastic elastomers, more particularly, thermoplastic block copolymers can be oil-extended to produce soft and flexible compositions. The oil plasticized thermoplastic block copolymer compositions of the prior art, however, suffers from one or more poor physical and mechanical properties such as poor breaking strength, poor elongation, poor craze, tear, creep, and crack resistance, and poor oil acceptance, to name a few. For instance, Shell Technical Bulletin No. SC 65-75 teaches the use of low viscosity poly(styrene-ethylene-butylene-styrene) triblock copolymers (Kraton G 1650 and G 1652) having styrene end block to ethylene and butylene center block ratio of 28:72 and 29:71 and with Brookfield Viscosities of 1,500 and 550 cps (viscosity being measured for a solution of 20 weight percent solids in toluene at 25.degree. C.) respectively in blends with butyl rubber, tackifier, filler, and oil. In none of the blends, however, are the properties of the compositions desirable; but rather, the use of other polymers such as butyl rubber, tackifiers, and fillers for extending and plasticizing the triblock copolymers result in dimensionally unstable mastic like materials which are not acceptable for purposes of the present invention. Furthermore, when the low viscosity triblock copolymers as disclosed in Shell's Bulletin No. SC 65-75 are plasticized with oil, the compositions obtained show decreases in the desired properties such as poor elongation and tensile strength, poor creep, craze, tear, and crack resistance; in addition, these compositions of the prior art trend to rupture and crumble when submitted to moderate shearing stress conditions.